The testing of mechanical properties of materials is a well-studied art. Standard tests exist for measuring mechanical properties such as Young's modulus, strain hardening exponent, yield strength, hardness, and the like, and many materials have been carefully characterized in terms of mechanical properties. One set of techniques for determining mechanical properties in materials involve tests in the macro regime in which, for example, a sample of material is stretched and its overall mechanical response inferred in terms of stress and deformation. These and other techniques have served, and continue to serve, an important role in determining critical mechanical properties so that careful processing and selection of materials for use in a variety of industrial settings can be made.
The above-described techniques, however, typically require large samples of material and generally are destructive of those samples. There is an increasing need in the field of materials science for analysis of small-scale samples in a manner that can be essentially non-destructive. The increasing rate of miniaturization in the semiconductor field, increasing interest in thin coatings for optical, electronic, magnetic, and mechanical devices, and increasing use of functionally-graded materials have led to a need for in situ testing of mechanical properties in small-scale structures. Additionally, there is interest in probing properties of individual phases, grain boundaries, and interfaces between phases and properties of novel materials such as nanocrystalline materials, or laminated or fibrous composites.
Indentation testing has developed as a viable technique for determining certain properties in a variety of materials at a very small scale, essentially non-destructively. Indentation testing typically involves placing a sample to be tested on a stage and applying a load to a surface of the sample via an indenter so as to slightly deform or penetrate the surface, followed by removal of the load. Several techniques can be employed to derive certain properties of the material from characteristics of the interaction of the indenter with the material. One set of techniques involves measuring an area of indentation during or after indentation, for example, optically, refractively, via surface profilometry, etc. U.S. Pat. Nos. 4,627,096 (Grattoni, et al.), 4,945,490 (Biddle, Jr. et al.), 5,284,049 (Fukumoto), 5,355,721 (Las Navas Garcia), 5,483,621 (Mazzoleni), 5,486,924 (Lacey), 4,852,397 (Haggag), 5,490,416 (Adler), 3,822,946 (Rynkowski), and others follow this procedure. For example, the measured area of indentation can be used to determine a simple "flow" or hardness value for the material, which is defined as the load applied divided by the projected area of the indentation. Or, the dimension of any cracks formed in the sample surface can be measured to determine the toughness of the material. Alternatively, the depth of penetration of the indenter as a function of applied load can be measured, and calculations performed to estimate roughly some mechanical properties. As discussed below, these techniques, in the prior art, have disadvantages.
Various shapes of indenters, for example spherical, cone-shaped, and pyramidal geometries can be used in indentation testing. Sharp indenters (e.g., cone-shaped and pyramidal) can be used in conventional tests to apply a load to a sample surface to form an imprint, or until the surface cracks, followed by measurement of the area of imprint or determination of the crack length to measure hardness or toughness, respectively. One piece of indentation testing equipment utilizing a sharp indenter at ultra low loads is sold by Nano Instruments, Inc. as the Nanoindenter.TM. indentation tester. The Nanoindenter.TM. is a relatively complex, self-contained unit including an indenter system, a sharp indenter, a light optical microscope, a moveable x-y table, and a computer. Analysis of load/depth curves with loads of less than one Newton and displacement of less than one .mu.m using a three-sided pyramidal indenter is most typically carried out.
Blunt indenters, for example those having a surface contacting the sample surface that is spherical, are advantageous for use in indentation testing under certain circumstances for several reasons. First, less sample-destructive analyses often can be carried out. However, with blunt (spherical) indenters, sensitivity problems are maximized since displacement of the sensor into the sample surface, at a particular applied load, is less than displacement with a sharp indenter. This is especially problematic in measuring very soft materials. Spherical indenters have, therefore, found most use in techniques in which load is applied to a sample surface and the diameter of the indentation formed thereby is measured using, for example, optical means.
U.S. Pat. No. 4,820,051 (Yanagisawa, et al.) discloses self-contained apparatus for measurement of the hardness of materials. A load is applied to a sample via a sharp indenter (having a tip with a radius of curvature between 0.01 and 0.1 .mu.m), and the displacement of the indenter relative to the sample is determined. An optical sensing mechanism determines the penetration depth of the indenter. Yanagisawa, et al. measure load/displacement values only during application of the load, with a self-contained unit, and measure only hardness of the material. Yanagisawa, et al. measure penetration and, with knowledge of the indenter geometry and assuming that no pile-up or sinking-in of the material at the contact perimeter occurs (which is known to be a factor that must be taken into account for accurate measurement), appear to calculate what the area of the indentation would be without sinking-in or pile-up, to measure hardness. Measurements are made in a load range of less than one Newton.
Gattoni, et al. (U.S. Pat. No. 4,627,096) recognize that sinking-in during indentation testing should be taken into account when measuring hardness of a sample (see, e.g., FIGS. 1 and 4). Therefore, Gattoni, et al. illuminate the sample carrying the impression and optical processing equipment is used to determine the contact area between the indenter and the sample.
U.S. Pat. No. 4,699,000 (Lashmore, et al. describes self-contained apparatus and methods for determining hardness. Displacement of the indenter into the sample as a function of time, using sharp indenter geometries, is made and a load versus displacement curve is thereby derived. Lashmore, et al., measure penetration and, with knowledge of the indenter geometry and assuming no pile-up or sinking-in, calculate the area of the indentation (column 5, lines 5-43) to measure hardness using a self-contained unit. The displacement sensor of Lashmore, et al. is quite removed spatially from the indenter (FIGS. 2, 3). Lashmore, et al. state that modulus, yield strength, impact, hardness, creep and fatigue also can be determined. No indication, however, is given as to how to go about determining these properties or whether, using the described techniques, accurate determination of these properties can be made.
U.S. Pat. No. 5,133,210 (Lesko, et al.) exploits thermal expansion in applying a load to a sample surface via a spherical indenter. Various measurements of load versus penetration (displacement) are made and theories are presented as to how various mechanical properties can be derived. However, Lesko, et al. do not take into account sinking-in or pile-up of material at the contact perimeter. Additionally, it appears from FIG. 5 of Lesko and theoretical analysis (Col. 5, lines 35-39 and Col. 4, lines 50-53) of Lesko, et al., that the assumption is made that the plastic regime of the load/displacement curve is linear. This assumption ignores the known non-linearity of the strain hardening exponent. Lesko, et al. do not show experimental data supporting the evaluation of Young's modulus from a load/displacement curve. Moreover, the displacement sensor is quite removed spatially from the indenter (FIG. 3 of Lesko). Only ball indenters, and self-contained units, are described. Measurements are made in the 1000 Newton range. It is unclear how the methodology of Lesko, et al. would be applied to measurement at low loads.
U.S. Pat. No. 5,490,416 (Adler) describes indentation of surfaces of materials using a spherical indenter to determine hardness. Load is applied to a sample via the indenter, but no load/depth relationship is experimentally obtained. In an effort to accurately take into account sinking-in and pile-up of material at the contact perimeter, a relatively time-consuming and labor-intensive process is carried out involving multiple indentation tests where the profile of the indentation is traced after each test with a surface analyzer to determine the depth and diameter of the indentation. Adler mentions that other devices may be used to measure the depth while load is being applied. However, no specific experimental arrangements are described in detail. No indication is given that any mechanical properties are measured directly from any portion of a load/displacement curve. Additionally, the theoretical framework relied upon assumes only plastic material properties.
U.S. Pat. No. 4,852,397 (Haggag) describes a self-contained field indentation microprobe that measures load and penetration depth data during both loading and unloading cycles to determine flow properties and fracture toughness of a structure. The described apparatus is specifically designed for use in the field to determine mechanical characteristics of large samples, for example, a damaged pressure vessel or tank car. Haggag uses ultrasonic analyzers to measure thickness, internal presence of cracks, and pile-up around indentation after testing, and uses a video camera to measure an indentation formed from load applied with a spherical indenter. Haggag states that the slope of the unloading portion of a load/displacement curve can be used as a measure of elastic properties, but nowhere does Haggag describe derivatization of area of indentation from a load/displacement measurement. Measurement in the kiloNewton range and above is made.
Accurate determination of the area of an indentation formed during indentation testing, especially during loading, can be critical to accurate determination of several mechanical properties of a sample. One drawback of prior art indentation testing techniques is that determination of the area of the indentation formed while load is applied either is not made precisely, or requires relatively complicated apparatus. Prior indentation testing typically involves either forming an indentation, removing the indenter, and observing the size of the imprint with, for example, an optical microscope, profilometer, or the like (which adds a step to analysis and cannot account for elastic rebound of the material after unloading, which typically is significant), or indentation depth is measured and the area of indentation calculated with mere knowledge of the geometry of the indenter (which is an approximation that fails to take into account material pile-up or sinking-in, which is almost always relevant and affects the evaluation of mechanical properties), or involves complicated optical apparatus (such as that used by Grattoni, et al., U.S. Pat. No. 4,627,096).
Additionally, most known techniques cannot accurately determine properties of a sample in the elastic and plastic regimes within a single test. Moreover, most prior art techniques involve load/displacement analysis either at very low loads (in the nano regime), or at very high loads (tens or hundreds of kilograms), but do not provide the capability of sampling load/displacement characteristics of a variety of materials over a very wide range of loads to determine local as well as bulk properties.
Therefore, it is an object of the invention to provide apparatus and methods for indentation testing that allows for simple, relatively uncomplicated and inexpensive, and accurate measurement of a variety of mechanical properties. It is another object of the invention to provide indentation testing apparatus that can determine several mechanical properties in a single test or series of tests accurately, and reproducibly. It is another object of the invention to provide indentation testing apparatus that can sample materials accurately at very low loads, but is also capable of operating over a wide range of loads so that mechanical characterization of a material in the bulk as well as local regime can be carried out. It is another object of the invention to provide such apparatus in which indenters of a variety of shapes and sizes can be used. It is another object of the invention to provide a methodology and corresponding theoretical framework directly coupled to in situ load/displacement measurement using a variety of indenter shapes and sizes to derive mechanical properties.